Grassmannian Geometry Meets Dynamic Mode Decomposition in DMD-GEN: A New Metric for Mode Collapse in Time Series Generative Models

Generative models like Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) often fail to capture the full diversity of their training data, leading to mode collapse. While this issue is well-explored in image generation, it remains underinvestigated for time series data. We introduce a new definition of mode collapse specific to time series and propose a novel metric, DMD-GEN, to quantify its severity. Our metric utilizes Dynamic Mode Decomposition (DMD), a data-driven technique for identifying coherent spatiotemporal patterns, and employs Optimal Transport between DMD eigenvectors to assess discrepancies between the underlying dynamics of the original and generated data. This approach not only quantifies the preservation of essential dynamic characteristics but also provides interpretability by pinpointing which modes have collapsed. We validate DMD-GEN on both synthetic and real-world datasets using various generative models, including TimeGAN, TimeVAE, and DiffusionTS. The results demonstrate that DMD-GEN correlates well with traditional evaluation metrics for static data while offering the advantage of applicability to dynamic data. This work offers for the first time a definition of mode collapse for time series, improving understanding, and forming the basis of our tool for assessing and improving generative models in the time series domain.

Gaussian Mixture Models Based Augmentation Enhances GNN Generalization

Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when training data is limited in size or diversity. To address these issues, we introduce a theoretical framework using Rademacher complexity to compute a regret bound on the generalization error and then characterize the effect of data augmentation. This framework informs the design of GMM-GDA, an efficient graph data augmentation (GDA) algorithm leveraging the capability of Gaussian Mixture Models (GMMs) to approximate any distribution. Our approach not only outperforms existing augmentation techniques in terms of generalization but also offers improved time complexity, making it highly suitable for real-world applications.

Post-Hoc Robustness Enhancement in Graph Neural Networks with Conditional Random Fields

Graph Neural Networks (GNNs), which are nowadays the benchmark approach in graph representation learning, have been shown to be vulnerable to adversarial attacks, raising concerns about their real-world applicability. While existing defense techniques primarily concentrate on the training phase of GNNs, involving adjustments to message passing architectures or pre-processing methods, there is a noticeable gap in methods focusing on increasing robustness during inference. In this context, this study introduces RobustCRF, a post-hoc approach aiming to enhance the robustness of GNNs at the inference stage. Our proposed method, founded on statistical relational learning using a Conditional Random Field, is model-agnostic and does not require prior knowledge about the underlying model architecture. We validate the efficacy of this approach across various models, leveraging benchmark node classification datasets.

Centrality Graph Shift Operators for Graph Neural Networks

Graph Shift Operators (GSOs), such as the adjacency and graph Laplacian matrices, play a fundamental role in graph theory and graph representation learning. Traditional GSOs are typically constructed by normalizing the adjacency matrix by the degree matrix, a local centrality metric. In this work, we instead propose and study Centrality GSOs (CGSOs), which normalize adjacency matrices by global centrality metrics such as the PageRank, $k$-core or count of fixed length walks. We study spectral properties of the CGSOs, allowing us to get an understanding of their action on graph signals. We confirm this understanding by defining and running the spectral clustering algorithm based on different CGSOs on several synthetic and real-world datasets. We furthermore outline how our CGSO can act as the message passing operator in any Graph Neural Network and in particular demonstrate strong performance of a variant of the Graph Convolutional Network and Graph Attention Network using our CGSOs on several real-world benchmark datasets.

Graph Neural Networks on Discriminative Graphs of Words

In light of the recent success of Graph Neural Networks (GNNs) and their ability to perform inference on complex data structures, many studies apply GNNs to the task of text classification. In most previous methods, a heterogeneous graph, containing both word and document nodes, is constructed using the entire corpus and a GNN is used to classify document nodes. In this work, we explore a new Discriminative Graph of Words Graph Neural Network (DGoW-GNN) approach encapsulating both a novel discriminative graph construction and model to classify text. In our graph construction, containing only word nodes and no document nodes, we split the training corpus into disconnected subgraphs according to their labels and weight edges by the pointwise mutual information of the represented words. Our graph construction, for which we provide theoretical motivation, allows us to reformulate the task of text classification as the task of walk classification. We also propose a new model for the graph-based classification of text, which combines a GNN and a sequence model. We evaluate our approach on seven benchmark datasets and find that it is outperformed by several state-of-the-art baseline models. We analyse reasons for this performance difference and hypothesise under which conditions it is likely to change.

Atlas-Chat: Adapting Large Language Models for Low-Resource Moroccan Arabic Dialect

We introduce Atlas-Chat, the first-ever collection of large language models specifically developed for dialectal Arabic. Focusing on Moroccan Arabic, also known as Darija, we construct our instruction dataset by consolidating existing Darija language resources, creating novel datasets both manually and synthetically, and translating English instructions with stringent quality control. Atlas-Chat-9B and 2B models, fine-tuned on the dataset, exhibit superior ability in following Darija instructions and performing standard NLP tasks. Notably, our models outperform both state-of-the-art and Arabic-specialized LLMs like LLaMa, Jais, and AceGPT, e.g., achieving a 13% performance boost over a larger 13B model on DarijaMMLU, in our newly introduced evaluation suite for Darija covering both discriminative and generative tasks. Furthermore, we perform an experimental analysis of various fine-tuning strategies and base model choices to determine optimal configurations. All our resources are publicly accessible, and we believe our work offers comprehensive design methodologies of instruction-tuning for low-resource language variants, which are often neglected in favor of data-rich languages by contemporary LLMs.

Bounding the Expected Robustness of Graph Neural Networks Subject to Node Feature Attacks

Graph Neural Networks (GNNs) have demonstrated state-of-the-art performance in various graph representation learning tasks. Recently, studies revealed their vulnerability to adversarial attacks. In this work, we theoretically define the concept of expected robustness in the context of attributed graphs and relate it to the classical definition of adversarial robustness in the graph representation learning literature. Our definition allows us to derive an upper bound of the expected robustness of Graph Convolutional Networks (GCNs) and Graph Isomorphism Networks subject to node feature attacks. Building on these findings, we connect the expected robustness of GNNs to the orthonormality of their weight matrices and consequently propose an attack-independent, more robust variant of the GCN, called the Graph Convolutional Orthonormal Robust Networks (GCORNs). We further introduce a probabilistic method to estimate the expected robustness, which allows us to evaluate the effectiveness of GCORN on several real-world datasets. Experimental experiments showed that GCORN outperforms available defense methods. Our code is publicly available at: \href{https://github.com/Sennadir/GCORN}{https://github.com/Sennadir/GCORN}.

A Simple and Yet Fairly Effective Defense for Graph Neural Networks

Graph Neural Networks (GNNs) have emerged as the dominant approach for machine learning on graph-structured data. However, concerns have arisen regarding the vulnerability of GNNs to small adversarial perturbations. Existing defense methods against such perturbations suffer from high time complexity and can negatively impact the model's performance on clean graphs. To address these challenges, this paper introduces NoisyGNNs, a novel defense method that incorporates noise into the underlying model's architecture. We establish a theoretical connection between noise injection and the enhancement of GNN robustness, highlighting the effectiveness of our approach. We further conduct extensive empirical evaluations on the node classification task to validate our theoretical findings, focusing on two popular GNNs: the GCN and GIN. The results demonstrate that NoisyGNN achieves superior or comparable defense performance to existing methods while minimizing added time complexity. The NoisyGNN approach is model-agnostic, allowing it to be integrated with different GNN architectures. Successful combinations of our NoisyGNN approach with existing defense techniques demonstrate even further improved adversarial defense results. Our code is publicly available at: https://github.com/Sennadir/NoisyGNN.